3 papers
math.MG2026
A doubling Loewner sphere that is not a quasisphere
Matthew Romney
We construct a metric 2-sphere of finite Hausdorff 2-measure that is doubling, linearly locally connected and Loewner but cannot be mapped to the standard sphere by a quasisymmetri…
math.MG2026
Metric geodesic covers of graphs
Jerry Chen, Kyle Hess, Matthew Romney
We study the problem of finding, for a given one-dimensional topological space , a cover of of smallest size by geodesics with respect to some metric. The infimal size of su…
math.MG2024
Graphs that are not minimal for conformal dimension
Matthew Romney
We construct functions whose graph as a subset of has Hausdorff dimension greater than any given value but conformal dimensio…